Ok, this just goes above and beyond being "neighborly". If you are allowed to have roosters and you want your rooster, then keep your rooster. You've done everything you can to minimize the noise to your neighbor.
Bottom line: She doesn't like you. So who cares if she doesn't like you more than she did before. I'm sure it will really hurt your rooster's feelings if you tell him the neighbor doesn't like him either.
She's just a miserable old PITA. $10 says if you got rid of your rooster, she'd be complaining about something else........your kids, your dog, your lawn, the color of your house, whatever. Just tell her you are within your rights to have a rooster and that is that. Don't listen to her complaining anymore.
Oh, and change your phone number to an unlisted # so she can't call you to complain.